TY - EJOUR
DO - 10.1007/s11134-016-9480-3
AB - In an M/M/1/C queue, customers are lost when they arrive to find C customers already present. Assuming that each arriving customer brings a certain amount of revenue, we are interested in calculating the value of an extra waiting place in terms of the expected amount of extra revenue that the queue will earn over a finite time horizon [0, t]. There are different ways of approaching this problem. One involves the derivation of Markov renewal equations, conditioning on the first instance at which the state of the queue changes; a second involves an elegant coupling argument; and a third involves expressing the value of capacity in terms of the entries of a transient analogue of the deviation matrix. In this paper, we shall compare and contrast these approaches and, in particular, use the coupling analysis to explain why the selling price of an extra unit of capacity remains the same when the arrival and service rates are interchanged when the queue starts at full capacity.
T1 - The roles of coupling and the deviation matrix in determining the value of capacity in M/M/1/C queues
IS - 1-2
DA - 2016
AU - Braunsteins, Peter
AU - Hautphenne, Sophie
AU - Taylor, Peter G.
JF - Queueing Systems
SP - 157-179
VL - 83
EP - 157-179
PB - Springer Verlag
PP - Dordrecht
ID - 219638
KW - M/M/1/C queue
KW - Coupling
KW - Deviation matrix
KW - Markov chain
SN - 0257-0130
UR - http://infoscience.epfl.ch/record/219638/files/BraunsteinsHautphenneTaylor2016.pdf
ER -